Questions: Solve for (x) (z=2x-3y)

Transcript text: Solve for $x$ \[ z=2 x-3 y \]

Solution

Solution Steps

To solve for $ x $ in the equation $ z = 2x - 3y $, we need to isolate $ x $ on one side of the equation. This involves rearranging the equation by performing algebraic operations.

Solution Approach

Add $ 3y $ to both sides of the equation to move the $ y $-term to the left side.
Divide both sides by 2 to solve for $ x $.

Step 1: Add $ 3y $ to both sides

Starting with the equation: \[ z = 2x - 3y \] we add $ 3y $ to both sides to isolate the term with $ x $: \[ z + 3y = 2x \]

Step 2: Divide both sides by 2

Next, we divide both sides of the equation by 2 to solve for $ x $: \[ x = \frac{z + 3y}{2} \]

Step 3: Substitute the given values

Given $ z = 10 $ and $ y = 2 $, we substitute these values into the equation: \[ x = \frac{10 + 3 \cdot 2}{2} \]

Step 4: Simplify the expression

Simplify the expression to find the value of $ x $: \[ x = \frac{10 + 6}{2} = \frac{16}{2} = 8.0 \]

Final Answer

\[ \boxed{x = \frac{z + 3y}{2}} \]

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